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A genetic algorithm based method is proposed to tune the parameters of a power system stabiliser (PSS). This method integrates the classical parameter optimisation approach, involving the solution of a Lyapunov equation, within a genetic search process. It also ensures that for any operating condition within a pre-defined domain, the system remains stable when subjected to small perturbations. The optimisation criterion employs a quadratic performance index that measures the quality of system dynamic response within the tuning process. The solution thus obtained is globally optimal and robust. The proposed method has been tested on two different PSS structures: the lead-lag PSS and the derivative PSS. System dynamic performances with PSS tuned using the proposed technique are highly satisfactory for different load conditions and system configurations.